学术报告

报告题目：The rigidity and gap theorem for Liouville's equation

报告人：沈伟明   首都师范大学

报告摘要：In this talk, we study the properties of the first global term in the polyhomogeneous expansions for Liouville's equation. We obtain rigidity and gap results for the boundary integral of the global coefficient. We prove that such a boundary integral is always nonpositive, and is zero if and only if the underlying domain is a disc. More generally, we prove some gap theorems relating such a boundary integral to the number of components of the boundary. The conformal structure plays an essential role. We also give some positive mass theorem type results through the integral of the global coefficient.

时间：2019年12月16日（星期一）下午2：00 — 3：00

地点：逸夫科研楼1537

报告人简介：

沈伟明，2016年博士毕业于北京大学数学系，北京国际数学研究中心博士后，2018年起在首都师范大学数学云顶yd222线路检测工作。主要研究领域是偏微分方程与几何分析。主要研究成果均发表在《J. Funct. Anal.》,《Advances in Math.》,《Sci. China Math.》,《Calc. Var. Partial Dif.》等国际著名数学期刊上。